CTNF 18/506,187 CTNF 100751 Notice of Pre-AIA or AIA Status 07-03-aia AIA 15-10-aia The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA. Claim Rejections - 35 USC § 101 07-04-01 AIA 07-04 35 U.S.C. 101 reads as follows: Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title. Claims 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to a judicial exception (i.e., a law of nature, a natural phenomenon, or an abstract idea) without significantly more. 101 Subject Matter Eligibility Analysis Step 1: Claims 1-20 are within the four statutory categories (a process, machine, manufacture or composition of matter). Step 2A Prong One, Step 2A Prong Two, and Step 2B Analysis: Step 2A Prong One asks if the claim recites a judicial exception (abstract idea, law of nature, or natural phenomenon). If the claim recites a judicial exception, analysis proceeds to Step 2A Prong Two, which asks if the claim recites additional elements that integrate the abstract idea into a practical application. If the claim does not integrate the judicial exception, analysis proceeds to Step 2B, which asks if the claim amounts to significantly more than the judicial exception. If the claim does not amount to significantly more than the judicial exception, the claim is not eligible subject matter under 35 U.S.C. 101. None of the claims represent an improvement to technology. Claims 1-7 are directed to a method consisting of a series of steps, meaning that it is directed to the statutory category of process. Claims 8-20 are directed to storage mediums and processors which are machines. Regarding claim 1, the following claim elements are abstract ideas: determining a set of persistent homology barcodes based on the multi way data using the processer (This is an abstract idea of a mental process. The limitation involves observing relationships among interconnected data points and representing how those relationships persist across varying conditions using corresponding barcodes or graphical indicators. For example, a person could observe a graph or chart of connected data points, visually identify which connections or structures persists as conditions change, and record those persistent relationships using bars, markings, or other symbolic representations. Such observation, evaluation, comparison, and visualization of relationships can practically be performed in the human mind or with the aid of pen and paper, and therefore falls within the mental process grouping of abstract ideas. See MPEP 2106.04(a)(2)(III).) ; identifying at least a first significant persistent homology barcode in the set of persistent homology barcodes, returning a representative cycle of the first significant persistent homology (This is an abstract idea of a mental process. The limitation involves reviewing a plot containing multiple barcode representations, identifying a significant barcode based on observed characteristics such as persistence or relative prominence, and tracing a corresponding representative relationship cycle associated with the selected barcode. For example, a person could observe a plot containing multiple bars representing persistent relationships, visually determine which bar appears most significant (e.g., longest or most isolated), and trace the associated connected relationship pattern represented by the selected bar. Such observation, evaluation, comparison, and identification of relationships can practically be performed in the human mind or with the aid of pen and paper, and therefore falls within the mental process grouping of abstract ideas.) and computing an orthonormal basis of the multiway data (This is an abstract idea of a mental process. The limitation involves organizing and mathematically arranging relationships among data points into structured coordinate representation for comparison and analysis. A person could manually organize observed relationships and calculate corresponding coordinate relationships or normalized directional components using mathematical reasoning and written calculations. Such mathematical evaluation and organization can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mental process grouping of abstract ideas.) ; obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement (This is an abstract idea of a mental process and a mathematical concept. The limitation recites mathematical calculations involving projections, orthogonal complements, and harmonic representations to analyze relationships among data points. For example, a person could review a plotted representative cycle, mathematically compare the relationships among the connected components, and calculate a corresponding projected representation using mathematical reasoning and basic computational tools. Such mathematical evaluation, comparison, and analysis of relationships can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mathematical concepts and mental process grouping of abstract ideas.) ; and determining a predictive setup for an experiment based on the harmonic representation (This is an abstract idea of a mental process. The limitation involves evaluating relationships identified from the harmonic representation and determining which factors or conditions are likely relevant for a proposed experiment. For example, a person could review identified relationship patterns and weighted factor relationships from a plot or structured analysis, judge which factors appear most relevant or predictive for a particular outcome, and determine a proposed experimental setup based on those observations. Such observation, evaluation, judgement, and recommendation generation can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mental process grouping of abstract ideas.) The following claim elements are additional elements which, taken alone or in combination with the other elements, do not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception: receiving at a processor an input set of multi way data, wherein the multi way data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome, and wherein each factor has a codependency on at least one other factor in the set of interconnected factors (The step of “receiving” is merely a generic data gathering operation that has been recognized by the courts as well-understood, routine, and conventional activity. The recited numerical representations, interconnected factors, and codependences merely describe the content of the gathered data being analyzed and therefore amounts to insignificant extra-solution activity.) outputting the predictive setup for the experiment to a user (The step of “outputting” information merely presents the results of the abstract idea and constitutes insignificant extra-solution activity.) . Regarding claim 2 , the rejection of claim 1 is incorporated herein. Further, claim 2 recites the following additional elements, which taken alone or in combination with other elements, do not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception: executing the experiment using the predictive setup (The step of “executing” the experiment merely applies the results of the abstract idea and therefore amounts to mere instructions to apply the judicial exception. Further, executing the experiment using the determined predictive setup constitutes insignificant post-solution activity.) . Regarding claim 3, the rejection of claim 3 is incorporated herein. Further, claim 3 recites the following abstract ideas: wherein determining the set of persistent homology barcodes includes building a combinatorial structure using the input set of multi way data using the processor (This is an abstract idea of a mental process. The limitation involves organizing and relating interconnected data points into a structured arrangement based on observed relationships among the data. For example, a person could review a set of related data points, observe which data points appear connected or related to one another, and organize those relationships into plotted or structured arrangement for further analysis. Such observation, evaluation, categorization, and organization of relationships can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mental process grouping of abstract ideas.) . Regarding claim 4 , the rejection of claim 3 is incorporated herein. Further, claim 4 recites the following additional elements, which taken alone or in combination with other elements, do not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception: wherein the combinatorial structure is one of a Vietoris-Rips structure, an alpha structure, and a Czech complex (This limitation merely identify particular types of mathematical structures or formats used in conjunction with the recited abstract idea and therefore amounts to insignificant extra-solution activity because they do not impose a meaningful limitation on the judicial exception or improve computer functionality.) . Regarding claim 5 , the rejection of claim 4 is incorporated herein. Further, claim 5 recites the following additional elements, which taken alone or in combination with other elements, do not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception: wherein the combinatorial structure forms a simplical complex (This limitation merely specifies a particular mathematical representation used in conjunction with the recited abstract idea and therefore amounts to insignificant extra-solution activity because it does not impose a meaningful limitation on the judicial exception or improve computer functionality.) . Regarding claim 6, the rejection of claim 1 is incorporated herein. Further, claim 6 recites the following abstract ideas: wherein identifying at least a first significant persistent homology barcode in the set of persistent homology barcode includes identifying a longest persistent homology barcode in the set of persistent homology barcodes (This an abstract idea of a mental process. The limitation involves reviewing multiple barcode representations, comparing relative lengths of the barcodes, and identifying the barcode that appears longest or most persistent. For example, a person could observe a plot containing multiple bars representing persistent relationships, visually compare the lengths of the bars, and determine which bars persists for the greatest range or duration. Such observation, comparison, evaluation, and identification can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mental process grouping of abstract ideas.) . Regarding claim 7, the rejection of claim 1 is incorporated herein. Further, claim 7 recites the following abstract ideas: wherein identifying at least a first significant persistent homology barcode in the set of persistent homology barcode includes identifying at least one of a longest bar, a starting point of a bar, and a bar positioned in a lowest density region of bars (This is an abstract idea of a mental process. The limitation involves reviewing barcode representations, visually comparing characteristics of the bars, and identifying bars based on observed properties such as relative length, position, or surrounding density. For example, a person could observe a plot containing multiple bars representing persistent relationships, visually determine which bar is longest, identify where a particular bar begins, or identify a bar located in a region having relatively fewer surrounding bars. Such observation, comparison, evaluation, and identification can practically be performed in the human mind or with the aid of pen and paper, and therefore falls within the mental process grouping of abstract ideas.) . Regarding claim 8, the following claim elements are abstract ideas: determining a set of persistent homology barcodes based on the multi way data using the processer (This is an abstract idea of a mental process. The limitation involves observing relationships among interconnected data points and representing how those relationships persist across varying conditions using corresponding barcodes or graphical indicators. For example, a person could observe a graph or chart of connected data points, visually identify which connections or structures persists as conditions change, and record those persistent relationships using bars, markings, or other symbolic representations. Such observation, evaluation, comparison, and visualization of relationships can practically be performed in the human mind or with the aid of pen and paper, and therefore falls within the mental process grouping of abstract ideas. See MPEP 2106.04(a)(2)(III).) ; identifying at least a first significant persistent homology barcode in the set of persistent homology barcodes, returning a representative cycle of the first significant persistent homology (This is an abstract idea of a mental process. The limitation involves reviewing a plot containing multiple barcode representations, identifying a significant barcode based on observed characteristics such as persistence or relative prominence, and tracing a corresponding representative relationship cycle associated with the selected barcode. For example, a person could observe a plot containing multiple bars representing persistent relationships, visually determine which bar appears most significant (e.g., longest or most isolated), and trace the associated connected relationship pattern represented by the selected bar. Such observation, evaluation, comparison, and identification of relationships can practically be performed in the human mind or with the aid of pen and paper, and therefore falls within the mental process grouping of abstract ideas.) and computing an orthonormal basis of the multiway data (This is an abstract idea of a mental process. The limitation involves organizing and mathematically arranging relationships among data points into structured coordinate representation for comparison and analysis. A person could manually organize observed relationships and calculate corresponding coordinate relationships or normalized directional components using mathematical reasoning and written calculations. Such mathematical evaluation and organization can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mental process grouping of abstract ideas.) ; obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement (This is an abstract idea of a mental process and a mathematical concept. The limitation recites mathematical calculations involving projections, orthogonal complements, and harmonic representations to analyze relationships among data points. For example, a person could review a plotted representative cycle, mathematically compare the relationships among the connected components, and calculate a corresponding projected representation using mathematical reasoning and basic computational tools. Such mathematical evaluation, comparison, and analysis of relationships can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mathematical concepts and mental process grouping of abstract ideas.) ; and determining a predictive setup for an experiment based on the harmonic representation (This is an abstract idea of a mental process. The limitation involves evaluating relationships identified from the harmonic representation and determining which factors or conditions are likely relevant for a proposed experiment. For example, a person could review identified relationship patterns and weighted factor relationships from a plot or structured analysis, judge which factors appear most relevant or predictive for a particular outcome, and determine a proposed experimental setup based on those observations. Such observation, evaluation, judgement, and recommendation generation can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mental process grouping of abstract ideas.) The following claim elements are additional elements which, taken alone or in combination with the other elements, do not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception: receiving at a processor an input set of multi way data, wherein the multi way data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome, and wherein each factor has a codependency on at least one other factor in the set of interconnected factors (The step of “receiving” is merely a generic data gathering operation that has been recognized by the courts as well-understood, routine, and conventional activity. The recited numerical representations, interconnected factors, and codependences merely describe the content of the gathered data being analyzed and therefore amounts to insignificant extra-solution activity.) a processor and a non-transitory memory (This a high-level recitation of generic computer components for performing the abstract idea. See MPEP 2106.05(f).) outputting the predictive setup for the experiment to a user (The step of “outputting” information merely presents the results of the abstract idea and constitutes insignificant extra-solution activity.) . Regarding claim 9, the rejection of claim 8 is incorporated herein. The claim recites similar limitations corresponding to claim 2. Therefore, the same subject matter analysis that was utilized for claim 2, as described above, is equally applicable to claim 9. Therefore, claim 9 is ineligible. Regarding claim 10, the rejection of claim 8 is incorporated herein. The claim recites similar limitations corresponding to claim 3. Therefore, the same subject matter analysis that was utilized for claim 3, as described above, is equally applicable to claim 10. Therefore, claim 10 is ineligible. Regarding claim 11, the rejection of claim 10 is incorporated herein. The claim recites similar limitations corresponding to claim 4. Therefore, the same subject matter analysis that was utilized for claim 4, as described above, is equally applicable to claim 11. Therefore, claim 11 is ineligible. Regarding claim 12, the rejection of claim 11 is incorporated herein. The claim recites similar limitations corresponding to claim 5. Therefore, the same subject matter analysis that was utilized for claim 5, as described above, is equally applicable to claim 12. Therefore, claim 12 is ineligible. Regarding claim 13, the rejection of claim 8 is incorporated herein. The claim recites similar limitations corresponding to claim 6. Therefore, the same subject matter analysis that was utilized for claim 6, as described above, is equally applicable to claim 13. Therefore, claim 13 is ineligible. Regarding claim 14, the rejection of claim 8 is incorporated herein. The claim recites similar limitations corresponding to claim 7. Therefore, the same subject matter analysis that was utilized for claim 7, as described above, is equally applicable to claim 14. Therefore, claim 14 is ineligible. Regarding claim 15, the following claim elements are abstract ideas: determining a set of persistent homology barcodes based on the multi way data using the processer (This is an abstract idea of a mental process. The limitation involves observing relationships among interconnected data points and representing how those relationships persist across varying conditions using corresponding barcodes or graphical indicators. For example, a person could observe a graph or chart of connected data points, visually identify which connections or structures persists as conditions change, and record those persistent relationships using bars, markings, or other symbolic representations. Such observation, evaluation, comparison, and visualization of relationships can practically be performed in the human mind or with the aid of pen and paper, and therefore falls within the mental process grouping of abstract ideas. See MPEP 2106.04(a)(2)(III).) ; identifying at least a first significant persistent homology barcode in the set of persistent homology barcodes, returning a representative cycle of the first significant persistent homology (This is an abstract idea of a mental process. The limitation involves reviewing a plot containing multiple barcode representations, identifying a significant barcode based on observed characteristics such as persistence or relative prominence, and tracing a corresponding representative relationship cycle associated with the selected barcode. For example, a person could observe a plot containing multiple bars representing persistent relationships, visually determine which bar appears most significant (e.g., longest or most isolated), and trace the associated connected relationship pattern represented by the selected bar. Such observation, evaluation, comparison, and identification of relationships can practically be performed in the human mind or with the aid of pen and paper, and therefore falls within the mental process grouping of abstract ideas.) and computing an orthonormal basis of the multiway data (This is an abstract idea of a mental process. The limitation involves organizing and mathematically arranging relationships among data points into structured coordinate representation for comparison and analysis. A person could manually organize observed relationships and calculate corresponding coordinate relationships or normalized directional components using mathematical reasoning and written calculations. Such mathematical evaluation and organization can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mental process grouping of abstract ideas.) ; obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement (This is an abstract idea of a mental process and a mathematical concept. The limitation recites mathematical calculations involving projections, orthogonal complements, and harmonic representations to analyze relationships among data points. For example, a person could review a plotted representative cycle, mathematically compare the relationships among the connected components, and calculate a corresponding projected representation using mathematical reasoning and basic computational tools. Such mathematical evaluation, comparison, and analysis of relationships can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mathematical concepts and mental process grouping of abstract ideas.) ; and determining a predictive setup for an experiment based on the harmonic representation (This is an abstract idea of a mental process. The limitation involves evaluating relationships identified from the harmonic representation and determining which factors or conditions are likely relevant for a proposed experiment. For example, a person could review identified relationship patterns and weighted factor relationships from a plot or structured analysis, judge which factors appear most relevant or predictive for a particular outcome, and determine a proposed experimental setup based on those observations. Such observation, evaluation, judgement, and recommendation generation can practically be performed in the human mind or with the aid of basic computational tools, and therefore falls within the mental process grouping of abstract ideas.) The following claim elements are additional elements which, taken alone or in combination with the other elements, do not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception: receiving at a processor an input set of multi way data, wherein the multi way data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome, and wherein each factor has a codependency on at least one other factor in the set of interconnected factors (The step of “receiving” is merely a generic data gathering operation that has been recognized by the courts as well-understood, routine, and conventional activity. The recited numerical representations, interconnected factors, and codependences merely describe the content of the gathered data being analyzed and therefore amounts to insignificant extra-solution activity.) a non-transitory computer readable storage medium (This a high-level recitation of generic computer components for performing the abstract idea. See MPEP 2106.05(f).) outputting the predictive setup for the experiment to a user (The step of “outputting” information merely presents the results of the abstract idea and constitutes insignificant extra-solution activity.) . Regarding claim 16, the rejection of claim 15 is incorporated herein. The claim recites similar limitations corresponding to claim 2. Therefore, the same subject matter analysis that was utilized for claim 2, as described above, is equally applicable to claim 16. Therefore, claim 16 is ineligible. Regarding claim 17, the rejection of claim 15 is incorporated herein. The claim recites similar limitations corresponding to claim 3. Therefore, the same subject matter analysis that was utilized for claim 3, as described above, is equally applicable to claim 17. Therefore, claim 17 is ineligible. Regarding claim 18, the rejection of claim 17 is incorporated herein. The claim recites similar limitations corresponding to claim 4. Therefore, the same subject matter analysis that was utilized for claim 4, as described above, is equally applicable to claim 18. Therefore, claim 18 is ineligible. Regarding claim 19, the rejection of claim 18 is incorporated herein. The claim recites similar limitations corresponding to claim 5. Therefore, the same subject matter analysis that was utilized for claim 5, as described above, is equally applicable to claim 19. Therefore, claim 19 is ineligible. Regarding claim 20, the rejection of claim 18 is incorporated herein. The claim recites similar limitations corresponding to claim 6. Therefore, the same subject matter analysis that was utilized for claim 6, as described above, is equally applicable to claim 20. Therefore, claim 20 is ineligible. Claim Rejections - 35 USC § 103 07-06 AIA 15-10-15 In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status. 07-20-aia AIA The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action: A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made. Claims 1-20 are rejected under the 35 U.S.C. 103 as being unpatentable over Cang et al. , (NPL: “Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening (Filed: 2017)) in view of Li et al., (NPL: “Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User’s Guide)) further in view of Aggarwal (Pub. No.: US 20040022445 A1 (Filed: 2002)). Regarding claim 1, Cang teaches: receiving at a processor an input set of multi way data, wherein the multi way data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome, and wherein each factor has a codependency on at least one other factor in the set of interconnected factors (Cang, [page 5] “multicomponent persistent homology barcodes are naturally a two-dimensional (2D) representation of biomolecules…Such approach addresses the nonlinear interactions among important element combinations while keeping the information from less important ones…We present multicomponent persistent homology, multi-level interactive persistent homology, vectorized persistent homology representation and electrostatic persistence. These formulations are crucial for the representability of persistent homology for biomolecules.” [page 5, section II.A] “For discrete data such as atomic coordinates in biomolecules, algebraic groups can be defined via simplicial complexes, which are constructed from simplices, generalizations of the geometric notion of nodes, edges, triangles and tetrahedrons to arbitrarily high dimensions. Homology characterizes the topological connectivity of geometric objects in terms of topological invariants” [page 7] “Various persistent homology techniques, including multicomponent, multi-level, multidimensional, multiresolution, electrostatic, and interactive persistent homologies have been designed either in our earlier work or in this paper for protein structural variability and complexity.”[page 26, conclusion] “Multi-level persistent homology allows tailored topological descriptions of any desirable interaction in biomolecules. Electrostatic persistence incorporates partial charges that are essential to biomolecules in topological invariants. These approaches are implemented via the appropriate construction of the distance matrix for filtration…Advanced machine learning methods…are utilized in the present work to facilitate the proposed topological methods in quantitative biomolecular predictions.” – Cang teaches processing biomolecular input data represented using “atomic coordinates”, “partial chargers,” and multi-dimensional topological representations, thereby teaching numerical representations of factors within multiway data. Cang further teaches “nonlinear interactions among important element combinations,” “multicomponent,” “multidimensional,” and “topological connectivity,” thereby teaching interconnected/codependent factors within a dataset. Cang additionally teaches machine-learning methods utilized in “quantitative biomolecular predictions,” thereby teaching that the interconnected factors affect predictive outcomes.) ; determining a set of persistent homology barcodes based on the multi way data using the processer (Cang, [page 12] “Computing persistence multiple times and stacking the results is especially useful when the parameters that are not chosen to be the filtration parameter are naturally discrete with underlying orders. For example, the multicomponent or element specific persistent homology will result in many persistent homology computations over different selections of atoms…multiple underlying dimensions exist in the element specific persistent homology characterization of molecules…Combining the dimension of spatial scale and dimension of element combinations, a 2D topological representation is obtained…With E = { E j } j = 1 N E denoting the collection of element combinations…and B d i m ( E i ) being the Betti- d i m barcodes obtained with atoms of element combination E j …” & “These images are directly used in deep convolutional neural networks for training and prediction.” – Cang teaches generating multiple persistent homology outputs from different combinations of biomolecular factors and dimensions, thereby teaching determining a set of persistent homology barcodes from the multiway input data. Cang further teaches organizing and stacking the resulting persistence outputs into multidimensional topological representations, thereby teaching generation of multiple barcode representations associated with different factor combinations. Cang additionally teaches using the resulting representations in CNN-based training and prediction systems, thereby teaching performing the barcode determination using a processor.) ; However, Cang does not teach but Cang in view of Li further in view of Aggarwal teaches the following limitations: identifying at least a first significant persistent homology barcode in the set of persistent homology barcodes, returning a representative cycle of the first significant persistent homology and computing an orthonormal basis of the multiway data (Cang, [page 11] “Another method of feature vector generation from a set of barcodes is to extract important statistics of barcode collections such as maximum values and standard deviations… F p S contains the same information with two extra terms, the birth and death values of the longest bar. Statistic feature vectors are collected from barcodes of three topological dimensions” [page 13] “The barcode space metrics can be directly used to assess the representation power of various persistent homology methods on biomolecules without potential overfitting effects induced by manually generated feature vectors. We show in the section of results that the barcode space metrics induced similarity measurement is significantly correlated to molecule functions.” Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator…For example, a representative for an interval L ∈ B a r c o d e 1 ( X ) consists of a closed curve or linear combination of closed curves which enclose a set of holes across the family of spaces” & “An important challenge, however, is that cycle representatives are not uniquely defined…We often want to find a cycle that captures not only the existence but also information about the location and shape of the hole that the homology class has detected.” Aggarwal, paragraph [0031] “The hyperplane R(P) can also be represented with the use of any point y on the hyperplane, and an orthonormal set of vectors E={e(1) . . . e(l)}, which lie on the hyperplane. We shall call (y, E) the axis representation of the hyperplane, whereas the set P is referred to as the point representation. Thus, R(P) (i.e., point representation) is the same as H(y, E) (i.e., axis representation). It is to be noted that there can be infinitely many point or axis representations of the same hyperplane.” – Cang teaches extracting important statistical characteristics from persistent homology barcodes, including maximum values and “the birth and death values of the longest bar,” and further teaches assessing barcode-space metrics that are “significantly correlated” to molecule functions, thereby teaching identifying a significant persistent homology barcode from the set of persistent homology barcodes under BRI. Li teaches finding a cycle representative corresponding to a homology class and further teaches that representatives for barcode intervals may consist of closed curves or combinations of closed curves, thereby teaching returning a representative cycle of the identified persistent homology barcode. Aggarwal teaches representing data using an orthonormal set of vectors forming an axis representation of a hyperplane, where the axis representation corresponds to the point representation, thereby reasonably teaching computing an orthonormal basis of the multiway data for projection processing under BRI.) ; obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement (Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator… For example, a representative for an interval L ∈ B a r c o d e 1 ( X ) consists of a closed curve or linear combination of closed curves which enclose a set of holes…” Aggarwal, paragraph [0031] “The hyperplane R(P) can also be represented with the use of any point y on the hyperplane, and an orthonormal set of vectors E={e(1) . . . e(l)}, which lie on the hyperplane. We shall call (y, E) the axis representation of the hyperplane, whereas the set P is referred to as the point representation.” - As discussed above, Li teaches representative cycles formed from closed curves or combinations of closed curves. Aggarwal teaches orthonormal vector-space representations and orthogonal projection operations using orthonormal vector sets. Aggarwal further teaches projecting data onto a subspace defined by an orthonormal set of vectors, which under BRI reasonably corresponds to projection into an orthogonal complement of the remaining vector space. Accordingly, the combined teachings reasonably teach obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement.) ; and determining a predictive setup for an experiment based on the harmonic representation and outputting the predictive setup for the experiment to a user (Cang, [page 26] “The representation power and reduction power of multicomponent persistent homology, multilevel persistent homology and electrostatic persistence are validated by two databases, namely PDBBind and DUD…Two classes of problems are used to test the proposed topological methods, including the regression (prediction) of protein-ligand binding affinities and the discrimination of active ligands from non-active decoys (virtual screening)… Advanced machine learning methods, including Wasserstein metric based k nearest neighbors (KNNs), gradient boosting trees (GBTs), random forest (RF), extra trees (ETs) and deep convolutional neural networks (CNNs) are utilized in the present work to facilitate the proposed topological methods in quantitative biomolecular predictions. The thorough examination of the method on the prediction of binding affinity for experimentally solved protein-ligand complexes leads to a structure-based virtual screening method, TopVS, which outperforms other modern methods.” Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator.” Aggarwal, paragraph [0028] “ The projection of a point x' onto this hyperplane is denoted by P(x, y, E) and is the closest approximation of x, which lies on this hyperplane.” – As discussed above, the combined teachings of Li and Aggarwal teach generating the claimed harmonic representation from representative-cycle projection processing under BRI. Cang further teaches using persistent homology-based topological representations from predictive biomolecular analysis, including regression prediction of protein-ligand binding affinities, discrimination of active ligands from decoys through virtual screening, and quantitative biomolecular predictions using machine learning methods, thereby teaching determining a predictive setup for an experiment based on the harmonic representation. Li further teaches that the resulting representative structural information “has meaning to the investigator,” thereby teaching that the generated predictive information is provided for interpretation and use by a human investigator/user of the analytical method under BRI.) . Accordingly, it would have been obvious to a person of ordinary skill in the art, before the effective filing date of the claimed invention, having Cang, Li, and Aggarwal before them, to incorporate the representative-cycle extraction techniques of Li and the orthonormal projection operations of Aggarwal into the persistent-homology-based predictive analysis framework of Cang. One would have been motivated to make such a combination in order to generate refined topological descriptors by forming representative cycles for significant homology classes and projecting those representative cycles into orthonormal subspace representations for use in predictive modeling. This would allow more consistent and structured topological features to be supplied to Cang’s regression and screening workflows, thereby supporting determination of predictive experimental setups based on the refined harmonic-style representations. Regarding claim 2 , Cang in view of Li further in view of Aggarwal teaches all the elements of claim 1, therefore is rejected for the same reasons as those presented for claim 1. Cang in view of Li further in view of Aggarwal further teaches: executing the experiment using the predictive setup (Cang, [page 5] “The aforementioned study of the characterization of small molecules and protein-ligand complexes leads to an optimal selection of features and models to be used for virtual screening. Finally, we consider the directory of useful decoys (DUD) database to examine the representability of our multicomponent persistent homology for virtual screening to distinguish actives from decoys.” & “For discrete data such as atomic coordinates in biomolecules, algebraic groups can be defined via simplicial complexes, which are constructed from simplices, generalizations of the geometric notion of nodes, edges, triangles and tetrahedrons to arbitrarily high dimensions.” Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator.” Aggarwal, [page 31] “ The hyperplane R(P) can also be represented with the use of any point y on the hyperplane, and an orthonormal set of vectors E={e(1) . . . e(l)}, which lie on the hyperplane.” - as discussed above with respect to claim1, the combined teachings of Cang, Li, and Aggarwal reasonably correspond under BRI to the general workflow illustrated in Figure 1 of the present application for generating predictive setups from multiway interaction data. Specifically, Cang teaches constructing simplicial-complex-based combinatorial structures from input biomolecular data and using those structures to generate persistent homology representations and predictive biomolecular analysis workflows. Li teaches returning representative cycles corresponding to identified homology classes and barcode intervals, while Aggarwal teaches orthonormal basis and projection operations that reasonably correspond to the claimed harmonic-style representative refinement under BRI. These teachings collectively correspond to the Figure 1 workflow of building combinatorial structures from input data, determining persistent homology barcodes, identifying significant bars, obtaining representative cycles, performing orthonormal projection processing, generating harmonic-style representative structures, and determining predictive setups from those structures. Cang further teaches applying the resulting predictive screening and analysis workflows to virtual-screening operations and experimentally solved protein-ligand complexes, thereby reasonably teaching executing the experiment using the previously determined predictive setup under BRI.). Regarding claim 3 , Cang in view of Li further in view of Aggarwal teaches all the elements of claim 1, therefore is rejected for the same reasons as those presented for claim 1. Cang in view of Li further in view of Aggarwal further teaches: wherein determining the set of persistent homology barcodes includes building a combinatorial structure using the input set of multi way data using the processor (Cang , [page 2, section II.A] “For discrete data such as atomic coordinates in biomolecules, algebraic groups can be defined via simplicial complexes, which are constructed from simplices, generalizations of the geometric notion of nodes, edges, triangles and tetrahedrons to arbitrarily high dimensions…. In persistent homology, Betti numbers are evaluated along with a filtration parameter, such as the radius of a ball or the level set of a hypersurface function, that continuously varies over an interval. Therefore, persistent homology is induced by the filtration.” [section II.A. 1] “ Simplicial complex A set of simplices K is a simplicial complex if all faces of any simplex in K are also in K and the intersection of any pair of simplices in K is either empty or a common face of the two simplices.” – Cang teaches constructing simplicial complexes from discrete biomolecular input data, where complexes are built from simplices such as nodes, edges, triangles, and tetrahedrons to form the topological representation used for persistent-homology analysis. Cang further teaches evaluating persistent-homology structures through filtration applied to these constructed complexes. Under BRI, constructing simplicial complexes from input data reasonably corresponds to building a combinatorial structure using the input set of multiway data using the processor prior to determining the persistent-homology barcodes.) . Regarding claim 4 , Cang in view of Li further in view of Aggarwal teaches all the elements of claim 3, therefore is rejected for the same reasons as those presented for claim 3. Cang in view of Li further in view of Aggarwal further teaches: wherein the combinatorial structure is one of a Vietoris-Rips structure, an alpha structure, and a Czech complex (Cang, [page 6] “Given a finite set of points X and a non-negative scale parameter r , the Vietoris-Rips complex and alpha complex are constructed as follows… The collection of all such simplices is the Vietoris-Rips complex of the finite metric space X … With A l p h a ( X , r ) being the alpha complex of X with the scale parameter r ” – Cang teaches constructing Vietoris-Rips complexes and apha complexes from finite point-set data for persistent-homology analysis. Under BRI, the claimed phrase “wherein the combinatorial structure is one of a Vietoris-Rips structure, an alpha structure, and a Czech complex” is reasonably interpreted as reciting alternative exemplary combinatorial-structure implementations, consistent with the present specification’s disclosure that “[t]he combinatorial structure can be built using a Vietoris-Rips complex, an alpha complex, a Čech complex model, or any similar combinatorial structure.”) . Regarding claim 5 , Cang in view of Li further in view of Aggarwal teaches all the elements of claim 4, therefore is rejected for the same reasons as those presented for claim 4. Cang in view of Li further in view of Aggarwal further teaches: wherein the combinatorial structure forms a simplical complex (Cang, [page 2] “For discrete data such as atomic coordinates in biomolecules, algebraic groups can be defined via simplicial complexes, which are constructed from simplices, generalizations of the geometric notion of nodes, edges, triangles and tetrahedrons to arbitrarily high dimensions.” & “ Simplicial complex A set of simplices K is a simplicial complex if all faces of any simplex in K are also in K and the intersection of any pair of simplices in K is either empty or a common face of the two simplices.” – teaches constructing simplicial complexes from simplices including nodes, edges, triangles, and tetrahedrons for persistent-homology analysis of biomolecular input data. Cang further defines a simplicial complex as a set of simplices satisfying simplicial-complex relationships between simplex faces and intersections. Under BRI, these teachings reasonably correspond to the claimed combinatorial structure forming a simplicial complex.) . Regarding claim 6 , Cang in view of Li further in view of Aggarwal teaches all the elements of claim 1, therefore is rejected for the same reasons as those presented for claim 1. Cang in view of Li further in view of Aggarwal further teaches: wherein identifying at least a first significant persistent homology barcode in the set of persistent homology barcode includes identifying a longest persistent homology barcode in the set of persistent homology barcodes (Cang, [page 11] “ Barcode statistics Another method of feature vector generation from a set of barcodes is to extract important statistics of barcode collections such as maximum values and standard deviations… F p S contains the same information with two extra terms, the birth and death values of the longest bar.” – Cang teaches extracting statistical characteristics from persistent homology barcode collections, including maximum values and specifically “the birth and death values of the longest bar.” Under BRI, the identified “longest bar” reasonably corresponds to identifying a longest persistent homology barcode from the set of persistent homology barcodes. Cang further teaches generating feature vectors from these barcode statistics for predictive biomolecular analysis workflows, thereby reasonably teaching identifying a significant persistent homology barcode including identifying the longest persistent homology barcode.) . Regarding claim 7 , Cang in view of Li further in view of Aggarwal teaches all the elements of claim 1, therefore is rejected for the same reasons as those presented for claim 1. Cang in view of Li further in view of Aggarwal further teaches: wherein identifying at least a first significant persistent homology barcode in the set of persistent homology barcode includes identifying at least one of a longest bar, a starting point of a bar, and a bar positioned in a lowest density region of bars (Cang, [page 10] “Additional, a charge density can be constructed… Equation (9) can be used for electrostatic filtration as well. In this case, the filtration parameter can be the charge density value and cubical complex based filtration can be used.” & “For a given set of atoms A, we denote its barcodes as B = { I α } α ϵ A and characterize each bar by an interval I α = [ b α , d α ] , where and are respectively the birth and death positions on the filtration axis. The length of each bar, or the persistence of topological invariant is given by… To locate the position position of all bars and persistences, we further split the set of barcodes on the filtration axis into a predefined N bins Bin” [page 11] “ Barcode statistics Another method of feature vector generation from a set of barcodes is to extract important statistics of barcode collections such as maximum values and standard deviations… F p S contains the same information with two extra terms, the birth and death values of the longest bar.” – Cang teaches characterizing persistent homology barcodes using intervals having birth and death positions on a filtration axis, where birth position reasonably corresponds under BRI to a starting point of a bar. Cang further teaches extracting barcode statistics including “the birth and death values of the longest bar,” thereby reasonably corresponding to identifying a longest bar. Cang also teaches density-based filtration because the filtration parameter may be a charge-density value, and further teaches splitting barcode collections into predefined bins along the filtration axis. Under BRI, using density-based filtration together with filtration-axis binning reasonably corresponds to identifying bars according to barcode regions, including bar positioned in a lowest density region of the bars. Accordingly, Cang reasonably teaches the claimed identifying step.) . Regarding claim 8 , Cang teaches the following limitations: receiving at a processor an input set of multiway data, wherein the multi way data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome, and wherein each factor has a codependency on at least one other factor in the set of interconnected factors (Cang, [page 5] “multicomponent persistent homology barcodes are naturally a two-dimensional (2D) representation of biomolecules…Such approach addresses the nonlinear interactions among important element combinations while keeping the information from less important ones…We present multicomponent persistent homology, multi-level interactive persistent homology, vectorized persistent homology representation and electrostatic persistence. These formulations are crucial for the representability of persistent homology for biomolecules.” [page 5, section II.A] “For discrete data such as atomic coordinates in biomolecules, algebraic groups can be defined via simplicial complexes, which are constructed from simplices, generalizations of the geometric notion of nodes, edges, triangles and tetrahedrons to arbitrarily high dimensions. Homology characterizes the topological connectivity of geometric objects in terms of topological invariants” [page 7] “Various persistent homology techniques, including multicomponent, multi-level, multidimensional, multiresolution, electrostatic, and interactive persistent homologies have been designed either in our earlier work or in this paper for protein structural variability and complexity.”[page 26, conclusion] “Multi-level persistent homology allows tailored topological descriptions of any desirable interaction in biomolecules. Electrostatic persistence incorporates partial charges that are essential to biomolecules in topological invariants. These approaches are implemented via the appropriate construction of the distance matrix for filtration…Advanced machine learning methods…are utilized in the present work to facilitate the proposed topological methods in quantitative biomolecular predictions.” – Cang teaches processing biomolecular input data represented using “atomic coordinates”, “partial chargers,” and multi-dimensional topological representations, thereby teaching numerical representations of factors within multiway data. Cang further teaches “nonlinear interactions among important element combinations,” “multicomponent,” “multidimensional,” and “topological connectivity,” thereby teaching interconnected/codependent factors within a dataset. Cang additionally teaches machine-learning methods utilized in “quantitative biomolecular predictions,” thereby teaching that the interconnected factors affect predictive outcomes.) ; determining a set of persistent homology barcodes based on the multi way data using the processer (Cang, [page 12] “Computing persistence multiple times and stacking the results is especially useful when the parameters that are not chosen to be the filtration parameter are naturally discrete with underlying orders. For example, the multicomponent or element specific persistent homology will result in many persistent homology computations over different selections of atoms…multiple underlying dimensions exist in the element specific persistent homology characterization of molecules…Combining the dimension of spatial scale and dimension of element combinations, a 2D topological representation is obtained…With E = { E j } j = 1 N E denoting the collection of element combinations…and B d i m ( E i ) being the Betti- d i m barcodes obtained with atoms of element combination E j …” & “These images are directly used in deep convolutional neural networks for training and prediction.” – Cang teaches generating multiple persistent homology outputs from different combinations of biomolecular factors and dimensions, thereby teaching determining a set of persistent homology barcodes from the multiway input data. Cang further teaches organizing and stacking the resulting persistence outputs into multidimensional topological representations, thereby teaching generation of multiple barcode representations associated with different factor combinations. Cang additionally teaches using the resulting representations in CNN-based training and prediction systems, thereby teaching performing the barcode determination using a processor.) ; However, Cang does not teach but Cang in view of Li further in view of Aggarwal teaches the following limitations: A computer system comprising: a processor and a non-transitory memory storing instructions for causing the computer system to perform the method of (Aggarwal, paragraph [0037] “Referring now to FIG. 1C, a block diagram illustrates a hardware implementation suitable for employing methodologies according to an embodiment of the present invention. As illustrated, an exemplary system comprises client devices 10 coupled via a large network 20 to a server 30. The server 30 may comprise a central processing unit (CPU) 32 coupled to a main memory 34 and a disk 36. The server 30 may also comprise a cache 38 in order to speed up calculations.” identifying at least a first significant persistent homology barcode in the set of persistent homology barcodes, returning a representative cycle of the first significant persistent homology and computing an orthonormal basis of the multiway data (Cang, [page 11] “Another method of feature vector generation from a set of barcodes is to extract important statistics of barcode collections such as maximum values and standard deviations… F p S contains the same information with two extra terms, the birth and death values of the longest bar. Statistic feature vectors are collected from barcodes of three topological dimensions” [page 13] “The barcode space metrics can be directly used to assess the representation power of various persistent homology methods on biomolecules without potential overfitting effects induced by manually generated feature vectors. We show in the section of results that the barcode space metrics induced similarity measurement is significantly correlated to molecule functions.” Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator…For example, a representative for an interval L ∈ B a r c o d e 1 ( X ) consists of a closed curve or linear combination of closed curves which enclose a set of holes across the family of spaces” & “An important challenge, however, is that cycle representatives are not uniquely defined…We often want to find a cycle that captures not only the existence but also information about the location and shape of the hole that the homology class has detected.” Aggarwal, paragraph [0031] “The hyperplane R(P) can also be represented with the use of any point y on the hyperplane, and an orthonormal set of vectors E={e(1) . . . e(l)}, which lie on the hyperplane. We shall call (y, E) the axis representation of the hyperplane, whereas the set P is referred to as the point representation. Thus, R(P) (i.e., point representation) is the same as H(y, E) (i.e., axis representation). It is to be noted that there can be infinitely many point or axis representations of the same hyperplane.” – Cang teaches extracting important statistical characteristics from persistent homology barcodes, including maximum values and “the birth and death values of the longest bar,” and further teaches assessing barcode-space metrics that are “significantly correlated” to molecule functions, thereby teaching identifying a significant persistent homology barcode from the set of persistent homology barcodes under BRI. Li teaches finding a cycle representative corresponding to a homology class and further teaches that representatives for barcode intervals may consist of closed curves or combinations of closed curves, thereby teaching returning a representative cycle of the identified persistent homology barcode. Aggarwal teaches representing data using an orthonormal set of vectors forming an axis representation of a hyperplane, where the axis representation corresponds to the point representation, thereby reasonably teaching computing an orthonormal basis of the multiway data for projection processing under BRI.) ; obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement (Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator… For example, a representative for an interval L ∈ B a r c o d e 1 ( X ) consists of a closed curve or linear combination of closed curves which enclose a set of holes…” Aggarwal, paragraph [0031] “The hyperplane R(P) can also be represented with the use of any point y on the hyperplane, and an orthonormal set of vectors E={e(1) . . . e(l)}, which lie on the hyperplane. We shall call (y, E) the axis representation of the hyperplane, whereas the set P is referred to as the point representation.” - As discussed above, Li teaches representative cycles formed from closed curves or combinations of closed curves. Aggarwal teaches orthonormal vector-space representations and orthogonal projection operations using orthonormal vector sets. Aggarwal further teaches projecting data onto a subspace defined by an orthonormal set of vectors, which under BRI reasonably corresponds to projection into an orthogonal complement of the remaining vector space. Accordingly, the combined teachings reasonably teach obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement.) ; and determining a predictive setup for an experiment based on the harmonic representation and outputting the predictive setup for the experiment to a user (Cang, [page 26] “The representation power and reduction power of multicomponent persistent homology, multilevel persistent homology and electrostatic persistence are validated by two databases, namely PDBBind and DUD…Two classes of problems are used to test the proposed topological methods, including the regression (prediction) of protein-ligand binding affinities and the discrimination of active ligands from non-active decoys (virtual screening)… Advanced machine learning methods, including Wasserstein metric based k nearest neighbors (KNNs), gradient boosting trees (GBTs), random forest (RF), extra trees (ETs) and deep convolutional neural networks (CNNs) are utilized in the present work to facilitate the proposed topological methods in quantitative biomolecular predictions. The thorough examination of the method on the prediction of binding affinity for experimentally solved protein-ligand complexes leads to a structure-based virtual screening method, TopVS, which outperforms other modern methods.” Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator.” Aggarwal, paragraph [0028] “ The projection of a point x' onto this hyperplane is denoted by P(x, y, E) and is the closest approximation of x, which lies on this hyperplane.” – As discussed above, the combined teachings of Li and Aggarwal teach generating the claimed harmonic representation from representative-cycle projection processing under BRI. Cang further teaches using persistent homology-based topological representations from predictive biomolecular analysis, including regression prediction of protein-ligand binding affinities, discrimination of active ligands from decoys through virtual screening, and quantitative biomolecular predictions using machine learning methods, thereby teaching determining a predictive setup for an experiment based on the harmonic representation. Li further teaches that the resulting representative structural information “has meaning to the investigator,” thereby teaching that the generated predictive information is provided for interpretation and use by a human investigator/user of the analytical method under BRI.) . Accordingly, it would have been obvious to a person of ordinary skill in the art, before the effective filing date of the claimed invention, having Cang, Li, and Aggarwal before them, to incorporate the representative-cycle extraction techniques of Li and the orthonormal projection operations of Aggarwal into the persistent-homology-based predictive analysis framework of Cang. One would have been motivated to make such a combination in order to generate refined topological descriptors by forming representative cycles for significant homology classes and projecting those representative cycles into orthonormal subspace representations for use in predictive modeling. This would allow more consistent and structured topological features to be supplied to Cang’s regression and screening workflows, thereby supporting determination of predictive experimental setups based on the refined harmonic-style representations. Regarding claim 9, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 8, therefore is rejected for the same reasons as those presented for claim 8. The claim recites similar limitations corresponding to claim 2 and is rejected for similar reasons as claim 2 using similar teachings and rationale. Regarding claim 10, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 8, therefore is rejected for the same reasons as those presented for claim 8. The claim recites similar limitations corresponding to claim 3 and is rejected for similar reasons as claim 3 using similar teachings and rationale. Regarding claim 11, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 10, therefore is rejected for the same reasons as those presented for claim 10. The claim recites similar limitations corresponding to claim 4 and is rejected for similar reasons as claim 4 using similar teachings and rationale. Regarding claim 12, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 11, therefore is rejected for the same reasons as those presented for claim 11. The claim recites similar limitations corresponding to claim 5 and is rejected for similar reasons as claim 5 using similar teachings and rationale. Regarding claim 13, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 8, therefore is rejected for the same reasons as those presented for claim 8. The claim recites similar limitations corresponding to claim 6 and is rejected for similar reasons as claim 6 using similar teachings and rationale. Regarding claim 14, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 8, therefore is rejected for the same reasons as those presented for claim 8. The claim recites similar limitations corresponding to claim 7 and is rejected for similar reasons as claim 7 using similar teachings and rationale. Regarding claim 15 , Cang teaches the following limitations: receiving at a processor an input set of multiway data, wherein the multi way data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome, and wherein each factor has a codependency on at least one other factor in the set of interconnected factors (Cang, [page 5] “multicomponent persistent homology barcodes are naturally a two-dimensional (2D) representation of biomolecules…Such approach addresses the nonlinear interactions among important element combinations while keeping the information from less important ones…We present multicomponent persistent homology, multi-level interactive persistent homology, vectorized persistent homology representation and electrostatic persistence. These formulations are crucial for the representability of persistent homology for biomolecules.” [page 5, section II.A] “For discrete data such as atomic coordinates in biomolecules, algebraic groups can be defined via simplicial complexes, which are constructed from simplices, generalizations of the geometric notion of nodes, edges, triangles and tetrahedrons to arbitrarily high dimensions. Homology characterizes the topological connectivity of geometric objects in terms of topological invariants” [page 7] “Various persistent homology techniques, including multicomponent, multi-level, multidimensional, multiresolution, electrostatic, and interactive persistent homologies have been designed either in our earlier work or in this paper for protein structural variability and complexity.”[page 26, conclusion] “Multi-level persistent homology allows tailored topological descriptions of any desirable interaction in biomolecules. Electrostatic persistence incorporates partial charges that are essential to biomolecules in topological invariants. These approaches are implemented via the appropriate construction of the distance matrix for filtration…Advanced machine learning methods…are utilized in the present work to facilitate the proposed topological methods in quantitative biomolecular predictions.” – Cang teaches processing biomolecular input data represented using “atomic coordinates”, “partial chargers,” and multi-dimensional topological representations, thereby teaching numerical representations of factors within multiway data. Cang further teaches “nonlinear interactions among important element combinations,” “multicomponent,” “multidimensional,” and “topological connectivity,” thereby teaching interconnected/codependent factors within a dataset. Cang additionally teaches machine- learning methods utilized in “quantitative biomolecular predictions,” thereby teaching that the interconnected factors affect predictive outcomes.) ; determining a set of persistent homology barcodes based on the multi way data using the processer (Cang, [page 12] “Computing persistence multiple times and stacking the results is especially useful when the parameters that are not chosen to be the filtration parameter are naturally discrete with underlying orders. For example, the multicomponent or element specific persistent homology will result in many persistent homology computations over different selections of atoms…multiple underlying dimensions exist in the element specific persistent homology characterization of molecules…Combining the dimension of spatial scale and dimension of element combinations, a 2D topological representation is obtained…With E = { E j } j = 1 N E denoting the collection of element combinations…and B d i m ( E i ) being the Betti- d i m barcodes obtained with atoms of element combination E j …” & “These images are directly used in deep convolutional neural networks for training and prediction.” – Cang teaches generating multiple persistent homology outputs from different combinations of biomolecular factors and dimensions, thereby teaching determining a set of persistent homology barcodes from the multiway input data. Cang further teaches organizing and stacking the resulting persistence outputs into multidimensional topological representations, thereby teaching generation of multiple barcode representations associated with different factor combinations. Cang additionally teaches using the resulting representations in CNN-based training and prediction systems, thereby teaching performing the barcode determination using a processor.) ; However, Cang does not teach but Cang in view of Li further in view of Aggarwal teaches the following limitations: A computer program product comprising: a non-transitory computer readable storage medium storing instructions for cause a computer system to perform operations comprising (Aggarwal, paragraph [0039] “ In one preferred embodiment, software components including instructions or code for performing the methodologies of the invention, as described herein, may be stored in one or more memory devices described above with respect to the server and, when ready to be utilized, loaded in part or in whole and executed by the CPU.” identifying at least a first significant persistent homology barcode in the set of persistent homology barcodes, returning a representative cycle of the first significant persistent homology and computing an orthonormal basis of the multiway data (Cang, [page 11] “Another method of feature vector generation from a set of barcodes is to extract important statistics of barcode collections such as maximum values and standard deviations… F p S contains the same information with two extra terms, the birth and death values of the longest bar. Statistic feature vectors are collected from barcodes of three topological dimensions” [page 13] “The barcode space metrics can be directly used to assess the representation power of various persistent homology methods on biomolecules without potential overfitting effects induced by manually generated feature vectors. We show in the section of results that the barcode space metrics induced similarity measurement is significantly correlated to molecule functions.” Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator…For example, a representative for an interval L ∈ B a r c o d e 1 ( X ) consists of a closed curve or linear combination of closed curves which enclose a set of holes across the family of spaces” & “An important challenge, however, is that cycle representatives are not uniquely defined…We often want to find a cycle that captures not only the existence but also information about the location and shape of the hole that the homology class has detected.” Aggarwal, paragraph [0031] “The hyperplane R(P) can also be represented with the use of any point y on the hyperplane, and an orthonormal set of vectors E={e(1) . . . e(l)}, which lie on the hyperplane. We shall call (y, E) the axis representation of the hyperplane, whereas the set P is referred to as the point representation. Thus, R(P) (i.e., point representation) is the same as H(y, E) (i.e., axis representation). It is to be noted that there can be infinitely many point or axis representations of the same hyperplane.” – Cang teaches extracting important statistical characteristics from persistent homology barcodes, including maximum values and “the birth and death values of the longest bar,” and further teaches assessing barcode-space metrics that are “significantly correlated” to molecule functions, thereby teaching identifying a significant persistent homology barcode from the set of persistent homology barcodes under BRI. Li teaches finding a cycle representative corresponding to a homology class and further teaches that representatives for barcode intervals may consist of closed curves or combinations of closed curves, thereby teaching returning a representative cycle of the identified persistent homology barcode. Aggarwal teaches representing data using an orthonormal set of vectors forming an axis representation of a hyperplane, where the axis representation corresponds to the point representation, thereby reasonably teaching computing an orthonormal basis of the multiway data for projection processing under BRI.) ; obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement (Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator… For example, a representative for an interval L ∈ B a r c o d e 1 ( X ) consists of a closed curve or linear combination of closed curves which enclose a set of holes…” Aggarwal, paragraph [0031] “The hyperplane R(P) can also be represented with the use of any point y on the hyperplane, and an orthonormal set of vectors E={e(1) . . . e(l)}, which lie on the hyperplane. We shall call (y, E) the axis representation of the hyperplane, whereas the set P is referred to as the point representation.” - As discussed above, Li teaches representative cycles formed from closed curves or combinations of closed curves. Aggarwal teaches orthonormal vector-space representations and orthogonal projection operations using orthonormal vector sets. Aggarwal further teaches projecting data onto a subspace defined by an orthonormal set of vectors, which under BRI reasonably corresponds to projection into an orthogonal complement of the remaining vector space. Accordingly, the combined teachings reasonably teach obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement.) ; and determining a predictive setup for an experiment based on the harmonic representation and outputting the predictive setup for the experiment to a user (Cang, [page 26] “The representation power and reduction power of multicomponent persistent homology, multilevel persistent homology and electrostatic persistence are validated by two databases, namely PDBBind and DUD…Two classes of problems are used to test the proposed topological methods, including the regression (prediction) of protein-ligand binding affinities and the discrimination of active ligands from non-active decoys (virtual screening)… Advanced machine learning methods, including Wasserstein metric based k nearest neighbors (KNNs), gradient boosting trees (GBTs), random forest (RF), extra trees (ETs) and deep convolutional neural networks (CNNs) are utilized in the present work to facilitate the proposed topological methods in quantitative biomolecular predictions. The thorough examination of the method on the prediction of binding affinity for experimentally solved protein-ligand complexes leads to a structure-based virtual screening method, TopVS, which outperforms other modern methods.” Li, [page 2] “A reasonable approach would be to find an element of the homology class, also known as a cycle representative, that witnesses structure in the data that has meaning to the investigator.” Aggarwal, paragraph [0028] “ The projection of a point x' onto this hyperplane is denoted by P(x, y, E) and is the closest approximation of x, which lies on this hyperplane.” – As discussed above, the combined teachings of Li and Aggarwal teach generating the claimed harmonic representation from representative-cycle projection processing under BRI. Cang further teaches using persistent homology-based topological representations from predictive biomolecular analysis, including regression prediction of protein-ligand binding affinities, discrimination of active ligands from decoys through virtual screening, and quantitative biomolecular predictions using machine learning methods, thereby teaching determining a predictive setup for an experiment based on the harmonic representation. Li further teaches that the resulting representative structural information “has meaning to the investigator,” thereby teaching that the generated predictive information is provided for interpretation and use by a human investigator/user of the analytical method under BRI.) . Accordingly, it would have been obvious to a person of ordinary skill in the art, before the effective filing date of the claimed invention, having Cang, Li, and Aggarwal before them, to incorporate the representative-cycle extraction techniques of Li and the orthonormal projection operations of Aggarwal into the persistent-homology-based predictive analysis framework of Cang. One would have been motivated to make such a combination in order to generate refined topological descriptors by forming representative cycles for significant homology classes and projecting those representative cycles into orthonormal subspace representations for use in predictive modeling. This would allow more consistent and structured topological features to be supplied to Cang’s regression and screening workflows, thereby supporting determination of predictive experimental setups based on the refined harmonic-style representations. Regarding claim 16, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 15, therefore is rejected for the same reasons as those presented for claim 15. The claim recites similar limitations corresponding to claim 2 and is rejected for similar reasons as claim 2 using similar teachings and rationale. Regarding claim 17, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 15, therefore is rejected for the same reasons as those presented for claim 15. The claim recites similar limitations corresponding to claim 3 and is rejected for similar reasons as claim 3 using similar teachings and rationale. Regarding claim 18, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 17, therefore is rejected for the same reasons as those presented for claim 17. The claim recites similar limitations corresponding to claim 4 and is rejected for similar reasons as claim 4 using similar teachings and rationale. Regarding claim 19, Cang in view of Li further in view of Aggarwal teaches all the elements of claim 18, therefore is rejected for the same reasons as those presented for claim 18. The claim recites similar limitations corresponding to claim 5 and is rejected for similar reasons as claim 5 using similar teachings and rationale. Regarding claim 20 , Cang in view of Li further in view of Aggarwal teaches all the elements of claim 18, therefore is rejected for the same reasons as those presented for claim 18. Cang in view of Li further in view of Aggarwal further teaches: wherein identifying at least a first significant persistent homology barcode in the set of persistent homology barcode includes identifying a longest persistent homology barcode in the set of persistent homology barcodes (Cang, [page 11] “ Barcode statistics Another method of feature vector generation from a set of barcodes is to extract important statistics of barcode collections such as maximum values and standard deviations… F p S contains the same information with two extra terms, the birth and death values of the longest bar.” – Cang teaches extracting statistical characteristics from persistent homology barcode collections, including maximum values and specifically “the birth and death values of the longest bar.” Under BRI, the identified “longest bar” reasonably corresponds to identifying a longest persistent homology barcode from the set of persistent homology barcodes. Cang further teaches generating feature vectors from these barcode statistics for predictive biomolecular analysis workflows, thereby reasonably teaching identifying a significant persistent homology barcode including identifying the longest persistent homology barcode.) . Conclusion Any inquiry concerning this communication or earlier communications from the examiner should be directed to Daravanh Phakousonh whose telephone number is (571)272-6324. The examiner can normally be reached Mon - Thurs 7 AM - 5 PM, Every other Friday 7 AM - 4PM. Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice. If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Li B Zhen can be reached at 571-272-3768. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300. Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000. /Daravanh Phakousonh/Examiner, Art Unit 2121 /Li B. Zhen/Supervisory Patent Examiner, Art Unit 2121 Application/Control Number: 18/506,187 Page 2 Art Unit: 2121 Application/Control Number: 18/506,187 Page 3 Art Unit: 2121 Application/Control Number: 18/506,187 Page 4 Art Unit: 2121 Application/Control Number: 18/506,187 Page 5 Art Unit: 2121 Application/Control Number: 18/506,187 Page 6 Art Unit: 2121 Application/Control Number: 18/506,187 Page 7 Art Unit: 2121 Application/Control Number: 18/506,187 Page 8 Art Unit: 2121 Application/Control Number: 18/506,187 Page 9 Art Unit: 2121 Application/Control Number: 18/506,187 Page 10 Art Unit: 2121 Application/Control Number: 18/506,187 Page 11 Art Unit: 2121 Application/Control Number: 18/506,187 Page 12 Art Unit: 2121 Application/Control Number: 18/506,187 Page 13 Art Unit: 2121 Application/Control Number: 18/506,187 Page 14 Art Unit: 2121 Application/Control Number: 18/506,187 Page 15 Art Unit: 2121 Application/Control Number: 18/506,187 Page 16 Art Unit: 2121 Application/Control Number: 18/506,187 Page 17 Art Unit: 2121 Application/Control Number: 18/506,187 Page 18 Art Unit: 2121 Application/Control Number: 18/506,187 Page 19 Art Unit: 2121 Application/Control Number: 18/506,187 Page 20 Art Unit: 2121 Application/Control Number: 18/506,187 Page 21 Art Unit: 2121 Application/Control Number: 18/506,187 Page 22 Art Unit: 2121 Application/Control Number: 18/506,187 Page 23 Art Unit: 2121 Application/Control Number: 18/506,187 Page 24 Art Unit: 2121 Application/Control Number: 18/506,187 Page 25 Art Unit: 2121 Application/Control Number: 18/506,187 Page 26 Art Unit: 2121 Application/Control Number: 18/506,187 Page 27 Art Unit: 2121 Application/Control Number: 18/506,187 Page 28 Art Unit: 2121 Application/Control Number: 18/506,187 Page 29 Art Unit: 2121 Application/Control Number: 18/506,187 Page 30 Art Unit: 2121 Application/Control Number: 18/506,187 Page 31 Art Unit: 2121 Application/Control Number: 18/506,187 Page 32 Art Unit: 2121 Application/Control Number: 18/506,187 Page 33 Art Unit: 2121 Application/Control Number: 18/506,187 Page 34 Art Unit: 2121 Application/Control Number: 18/506,187 Page 35 Art Unit: 2121 Application/Control Number: 18/506,187 Page 36 Art Unit: 2121 Application/Control Number: 18/506,187 Page 37 Art Unit: 2121 Application/Control Number: 18/506,187 Page 38 Art Unit: 2121 Application/Control Number: 18/506,187 Page 39 Art Unit: 2121 Application/Control Number: 18/506,187 Page 40 Art Unit: 2121 Application/Control Number: 18/506,187 Page 41 Art Unit: 2121 Application/Control Number: 18/506,187 Page 42 Art Unit: 2121 Application/Control Number: 18/506,187 Page 43 Art Unit: 2121
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